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CATEGORIES:Combinatorics Seminar
SUMMARY:Hypergraph Saturation Irregularities - Natalie Beh
ague (QMUL)
DTSTART;TZID=Europe/London:20180222T143000
DTEND;TZID=Europe/London:20180222T153000
UID:TALK100435AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/100435
DESCRIPTION:We say that a graph G is saturated with respect to
some graph F if G doesn't contain any copies of F
but adding any new edge to G creates some copy of
F. The saturation number sat(F\,n) is the minimum
number of edges an F-saturated graph on n vertice
s can have. This forms an interesting counterpoint
to the Turan number\; the saturation number is in
many ways less well-behaved. For example\, Tuza c
onjectured that sat(F\,n)/n must tend to a limit a
s n tends to infinity and this is still open. Howe
ver\, Pikhurko disproved a strengthening of Tuza's
\nconjecture by finding a finite family of graphs\
, whose saturation number divided by n does not te
nd to a limit. We will prove a similar result for
hypergraphs\nand discuss some variants.\n
LOCATION:MR12
CONTACT:Andrew Thomason
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